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The depth of the semigroup of balanced endomorphisms

Part of: Semigroups

Published online by Cambridge University Press:  26 February 2010

John B. Fountain
John B. Fountain
Affiliation:
Department of Mathematics, University of York, Heslington, York. YOI 5DD.
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Extract

Let X be an infinite set and T(X) be the full transformation semigroup on X. In [4] and [6] Howie gives a description of the subsemigroup of T(X) generated by its idempotents. In order to do this he defines, for α in T(X),

and refers to the cardinals s(α) = |S(α)|, d(α) = |Z(α)| and |c(α) = |C(α)| as the shift, the defect, and the collapse of α respectively. Then putting

he proves that the subsemigroup of T(X) generated by its idempotents is . Furthermore, both F and Q are generated by their idempotents

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Mathematika , Volume 41 , Issue 1 , June 1994 , pp. 199 - 208
Copyright
Copyright © University College London 1994

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References

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